Not sure where your clink info comes from Q but according to the BBC web site here the prison certainly predates your 1515 quote. hers's an extract from the site for those not wishing to read it all

The Clink Prison Museum is built on the foundations of one of the original prisons owned by the Bishop of Winchester. It is thought it got its name from the clinking of the manacles, fetters, chains and bolts that were used there. It was also the origin of the phrase "In the Clink", to mean in prison.

A short history

There has been a prison owned by the Bishop of Winchester in one form or another since the year 860, although at that time it would only have been one cell in a priests college. By 1076 an Archbishop had listed the type of punishments allowed, scourging with rods, solitary confinement, and bread and water in silence.

The building of a chapel and mansion at Southwark was begun in 1107 by the then current Bishop of Winchester, but was not completed until 1144, by his successor. There were two prisons included, one for men and one for women. It would have been a good source of income for the Bishop, as it was about this time that the whorehouses1 were regulated, bringing in plenty of fines and customers. The whorehouses were closed, reopened, moved and used throughout the life of the Clink, bringing in prisoners at a fairly steady rate. By 1180 the land was owned outright by the Clink prison.